Question: Nadia is 6 years older than Jessica. Nadia and Jessica first met 3 years ago. Six years ago, Nadia was 4 times as old as Jessica. How old is Nadia now?
We can use the given information to write down two equations that describe the ages of Nadia and Jessica. Let Nadia's current age be $n$ and Jessica's current age be $j$ The information in the first sentence can be expressed in the following equation: $n = j + 6$ Six years ago, Nadia was $n - 6$ years old, and Jessica was $j - 6$ years old. The information in the second sentence can be expressed in the following equation: $n - 6 = 4(j - 6)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $n$ , it might be easiest to solve our first equation for $j$ and substitute it into our second equation. Solving our first equation for $j$ , we get: $j = n - 6$ . Substituting this into our second equation, we get the equation: $n - 6 = 4($ $(n - 6)$ $ -$ $ 6)$ which combines the information about $n$ from both of our original equations. Simplifying the right side of this equation, we get: $n - 6 = 4n - 48$ Solving for $n$ , we get: $3 n = 42$ $n = 14$.